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Neural Inverse Operators for solving PDE Inverse Problems [PDF]

CoRR, 2023
Data and models for the paper "Neural Inverse Operators for solving PDE Inverse Problems"
Roberto Molinaro, Yunan Yang, Björn Engquist, Siddhartha Mishra   +3 more
core   +9 more sources

The finite element neural network method to simulate two dimensional partial differential equations and perform parameter identification [PDF]

Scientific Reports
Neural networks (NNs) have received growing interest in engineering due to their ability to assimilate high-dimensional data and provide accurate approximations for complex systems.
Mohammed Abda, Lucas Berthet, Mohsen Hamedi, Dani Hibatullah, Elsa Piollet, Christopher Blake, Bruno Blais, Frédérick P. Gosselin   +7 more
doaj   +2 more sources

QEKI: A Quantum–Classical Framework for Efficient Bayesian Inversion of PDEs [PDF]

Entropy
Solving Bayesian inverse problems efficiently stands as a major bottleneck in scientific computing. Although Bayesian Physics-Informed Neural Networks (B-PINNs) have introduced a robust way to quantify uncertainty, the high-dimensional parameter spaces ...
Jiawei Yong, Sihai Tang
doaj   +2 more sources

Remarks on control and inverse problems for PDEs

SeMA Journal
Abstract This paper deals with recent results and open questions on the control and parameter identification of systems governed by PDEs. Among them, we find a few parabolic and hyperbolic equations, sometimes in the framework of a free-boundary problem. In the considered control problems, we try to govern the behavior of the solution(
Enrique Fernández Cara
exaly   +3 more sources

Gaussian Process Regression for Inverse Problems in Linear PDEs

IFAC-PapersOnLine
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors defined based on advanced commutative algebra and algebraic analysis. The implementation of these priors is algorithmic
Bogdan Raiƫă, Markus Lange-Hegermann
exaly   +3 more sources

Enhancing Computational Accuracy in Surrogate Modeling for Elastic–Plastic Problems by Coupling S-FEM and Physics-Informed Deep Learning

Mathematics, 2023
Physics-informed neural networks (PINNs) provide a new approach to solving partial differential equations (PDEs), while the properties of coupled physical laws present potential in surrogate modeling.
Meijun Zhou, Gang Mei, Nengxiong Xu
doaj   +1 more source

Structured Random Sketching for PDE Inverse Problems [PDF]

SIAM Journal on Matrix Analysis and Applications, 2020
For an overdetermined system $\mathsf{A}\mathsf{x} \approx \mathsf{b}$ with $\mathsf{A}$ and $\mathsf{b}$ given, the least-square (LS) formulation $\min_x \, \|\mathsf{A}\mathsf{x}-\mathsf{b}\|_2$ is often used to find an acceptable solution $\mathsf{x}$.
Ke Chen, Qin Li 0007, Kit Newton, Stephen J. Wright 0001   +3 more
openaire   +3 more sources

Inverse coefficient problem for differential equation in partial derivatives of a fourth order in time with integral over-determination

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity.
M.J. Huntul, I. Tekin
doaj   +1 more source

Inverse Source Problems for Degenerate Time-Fractional PDE [PDF]

Progress in Fractional Differentiation and Applications, 2022
12 pages, 8 ...
Al-Salti, Nasser, Karimov, Erkinjon
openaire   +2 more sources

PINNs algorithm and its application in geotechnical engineering

Yantu gongcheng xuebao, 2021
The physical information neural networks (PINNs) algorithm, a new mesh-free algorithm, uses the automatic differential method to embed the partial differential equation directly into the neural networks so as to realize the intelligent solution of the ...
LAN Peng 1, LI Hai-chao 1, YE Xin-yu 1, ZHANG Sheng 1, SHENG Dai-chao 1, 2
doaj   +1 more source